(a) Group-Ranking Methods and Algorithms
(b) More Group-Ranking Methods and Paradoxes
(c) Arrow's Conditions and Approval Voting
(d) Weighted Voting and Voting Power
What are the differences between the Plurality, Run-off, Sequential Run-Off, Borda Count, and Condorcet methods?
What are the applications of weighted voting, voting power, and winning coalitions?
Hold in-class election.
Have students conduct an interest survey poll, i.e. ice cream, cars, music, etc.
Calculator/Computer Activities
Quiz
Test
Discrete Math
Unit II
Fair Division
(a) Estate Division
(b) Apportionment Algorithms
(c) More Apportionment Algorithms and Paradoxes
(d) Fair Division Algorithms: The Continuous
(e) Mathematical Induction
How do you determine fair division?
How do you determine estate division?
What are the similarities and differences of the Hamilton, Jefferson, Webster, Hill, and Adams apportionment methods?.
How do you prove word problems and algebraic situations using math induction?
Hold a mock distribution of items in a will.
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit III
Matrix Operations and Applications
(a) Addition and Subtraction of Matrices
(b) Multiplication of Matrices
(c) Population Growth: The Leslie Model
(d) Markov Chains
How do you add, subtract, multiply matrices?
How do you find the determinant?
How do you solve systems of equations using matrix methods?
How do you solve communication networks/mapping situations using matrices?
How do you solve problems using a Leslie Matrix?
How do you produce coordinate transformations?
How do you rotate, translate, and re-size coordinate shapes using matrices?
How do you determine harvesting strategies to stabilize a population using matrices?
How do you analyze data in matrix form?
How do you solve linear systems using matrices?
How do you solve word problems using Markov Chains?
Have students create a matrix art project
including a matrix of at least 8 points to demonstrate size, rotation, reflection,
and composite transformations.
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit IV
Graphs and Their Applications
(a) Modeling Projects
(b) Critical Paths
(c) The Vocabulary and Representations of Graphs
(d) Euler Circuits and Paths
(e) Hamiltonian Circuits and Paths
(f) Graph Coloring
What are the graph theory vocabulary terms location in various shapes?
What is the difference between finite and adjacency matrices?
What are the differences and similarities between critical paths, Euler circuits/paths, and Hamiltonian circuits/paths?
How do you find a minimum spanning tree?
How can the four color theorem be used to determine the chromatic number of various graphs?
What is the purpose of using Polish and Reverse Polish notation and how can you use it to solve problems?
Create a matrix picture and determine
whether or not it is complete.
Create an Icosian
Gameboard .
Plan a major event(wedding, buying a house) and determine critical path.
Plan a vacation or business trip using internet (Traveling Salesperson Problem).
Use the internet to study Euler and Hamiltonian circuits and paths.
Explore the internet for career and personality tests. Use the results to create career oriented word problems, i.e. students will create a word problem for a fashion designer that uses a Hamilton circuit.
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit V
More Graphs, Subgraphs, and Trees
(a) Planarity and Coloring
(b) The Traveling Salesperson Problem
(c) Finding the Shortest Route
(d) Trees and Their Properties
(e) Minimum Spanning Trees
(f) Binary Trees, Expression Trees, and Traversals
Counting and Probability
(a) Counting Techniques
(b) Probability
How are Venn diagrams useful when solving problems dealing with probability?
How do you solve probability problems using the addition and multiplication principles?
How do you solve problems using permutations, combinations, dependent, independent, circular, and mutually exclusive problems?
What are the differences between experimental and simulation probability models?
How do you find expected and discrete random values?
How do you solve problems using the Binomial Probability Theorem?
Have students create a portfolio of problems on a certain topic (i.e. M&M?s, dice, etc.)
Calculator/Computer Activities
Quiz
Test
Statistics Unit I
PRODUCING DATA
I. How Do We Get "Good" Data?
(a) Where do Data Come From?
(b) Measuring
(c) Do the Numbers Make Sense?
II. Sampling and Surveys
(a) Samples, Good and Bad
(b) What Do Samples Tell Us?
(c) Sample Surveys in the Real World
III. Designing Experiments
(a) Experiments, Good and Bad
(b) Experiments in the Real World
(c) Data Ethics
Statistics Unit II
ORGANIZING DATA
I. Describing Distributions
(a) Graphs, Good and Bad
(b) Displaying Distributions with Graphs
(c) Describing Distributions with Numbers
II. The Normal Distributions and Government Statistics
(a) Normal Distributions
(b) The Consumer Price Index and Government Statistics
III. Describing Relationships
(a) Scatterplots and Correlation
(b) Regression, Prediction, and Causation
In a given set of data, identify the individuals and variables; identify each variable as categorical or quantative.
In a given set of data, describe the overall pattern by giving numerical measures of center and spread and a description of shape.
Given a graphical distribution, is the distribution symmetric or skewed?
Given a set of data, which measures of center and spread are more appropriate: the mean and standard deviation or the fine-number summary?
Given a normal distribution with a stated mean and standard deviation, calculate the proportion of values above the given number, below the given number, and between two given numbers. Find the point with a stated proportion of all values above it.
Given a set of data, what is the correlation coefficient? Is there a positive or negative association, a linear pattern? Are there any outliers?
How do you find the slope and intercept of the least-squares regression line from the means and standard deviation of x and y and their correlation??
How does one calculate the residuals? How does the graph of the residuals allow one to determine if the data is truly a linear relationship?
Given a two-way table, find the marginal and conditional distributions.
Statistics Unit III
CHANCE
I. Chance and Probability
(a) Thinking about Chance
(b) Probability Models
II. Simulation and Expected Values
(a) Simulation
(b) Expected Values
Statistics Unit IV
INFERENCE
I. Introduction to Inference
(a) What Is a Confidence Interval?
(b) What is a Test of Significance
(c) Use and Abuse of Statistical Inference
II. Inference for Tables and Means
(a) Two-Way Tables and the Chi-Square Test
(b) Inference about a Population Mean
Table of Contents
Discrete Math
Unit 1
(a) Group-Ranking Methods and Algorithms
(b) More Group-Ranking Methods and Paradoxes
(c) Arrow's Conditions and Approval Voting
(d) Weighted Voting and Voting Power
What are the applications of weighted voting, voting power, and winning coalitions?
Have students conduct an interest survey poll, i.e. ice cream, cars, music, etc.
Calculator/Computer Activities
Quiz
Test
Discrete Math
Unit II
(a) Estate Division
(b) Apportionment Algorithms
(c) More Apportionment Algorithms and Paradoxes
(d) Fair Division Algorithms: The Continuous
(e) Mathematical Induction
How do you determine estate division?
What are the similarities and differences of the Hamilton, Jefferson, Webster, Hill, and Adams apportionment methods?.
How do you prove word problems and algebraic situations using math induction?
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit III
(a) Addition and Subtraction of Matrices
(b) Multiplication of Matrices
(c) Population Growth: The Leslie Model
(d) Markov Chains
How do you find the determinant?
How do you solve systems of equations using matrix methods?
How do you solve communication networks/mapping situations using matrices?
How do you solve problems using a Leslie Matrix?
How do you produce coordinate transformations?
How do you rotate, translate, and re-size coordinate shapes using matrices?
How do you determine harvesting strategies to stabilize a population using matrices?
How do you analyze data in matrix form?
How do you solve linear systems using matrices?
How do you solve word problems using Markov Chains?
including a matrix of at least 8 points to demonstrate size, rotation, reflection,
and composite transformations.
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit IV
(a) Modeling Projects
(b) Critical Paths
(c) The Vocabulary and Representations of Graphs
(d) Euler Circuits and Paths
(e) Hamiltonian Circuits and Paths
(f) Graph Coloring
What is the difference between finite and adjacency matrices?
What are the differences and similarities between critical paths, Euler circuits/paths, and Hamiltonian circuits/paths?
How do you find a minimum spanning tree?
How can the four color theorem be used to determine the chromatic number of various graphs?
What is the purpose of using Polish and Reverse Polish notation and how can you use it to solve problems?
whether or not it is complete.
Create an Icosian
Gameboard .
Plan a major event(wedding, buying a house) and determine critical path.
Plan a vacation or business trip using internet (Traveling Salesperson Problem).
Use the internet to study Euler and Hamiltonian circuits and paths.
Explore the internet for career and personality tests. Use the results to create career oriented word problems, i.e. students will create a word problem for a fashion designer that uses a Hamilton circuit.
Calculator/Computer Activities
Quiz
Test
Discrete Math Unit V
(a) Planarity and Coloring
(b) The Traveling Salesperson Problem
(c) Finding the Shortest Route
(d) Trees and Their Properties
(e) Minimum Spanning Trees
(f) Binary Trees, Expression Trees, and Traversals
Discrete Math
Unit VI
(a) Counting Techniques
(b) Probability
How do you solve probability problems using the addition and multiplication principles?
How do you solve problems using permutations, combinations, dependent, independent, circular, and mutually exclusive problems?
What are the differences between experimental and simulation probability models?
How do you find expected and discrete random values?
How do you solve problems using the Binomial Probability Theorem?
Calculator/Computer Activities
Quiz
Test
Statistics Unit I
I. How Do We Get "Good" Data?
(a) Where do Data Come From?
(b) Measuring
(c) Do the Numbers Make Sense?
II. Sampling and Surveys
(a) Samples, Good and Bad
(b) What Do Samples Tell Us?
(c) Sample Surveys in the Real World
III. Designing Experiments
(a) Experiments, Good and Bad
(b) Experiments in the Real World
(c) Data Ethics
Statistics Unit II
I. Describing Distributions
(a) Graphs, Good and Bad
(b) Displaying Distributions with Graphs
(c) Describing Distributions with Numbers
II. The Normal Distributions and Government Statistics
(a) Normal Distributions
(b) The Consumer Price Index and Government Statistics
III. Describing Relationships
(a) Scatterplots and Correlation
(b) Regression, Prediction, and Causation
In a given set of data, describe the overall pattern by giving numerical measures of center and spread and a description of shape.
Given a graphical distribution, is the distribution symmetric or skewed?
Given a set of data, which measures of center and spread are more appropriate: the mean and standard deviation or the fine-number summary?
Given a normal distribution with a stated mean and standard deviation, calculate the proportion of values above the given number, below the given number, and between two given numbers. Find the point with a stated proportion of all values above it.
Given a set of data, what is the correlation coefficient? Is there a positive or negative association, a linear pattern? Are there any outliers?
How do you find the slope and intercept of the least-squares regression line from the means and standard deviation of x and y and their correlation??
How does one calculate the residuals? How does the graph of the residuals allow one to determine if the data is truly a linear relationship?
Given a two-way table, find the marginal and conditional distributions.
Statistics Unit III
I. Chance and Probability
(a) Thinking about Chance
(b) Probability Models
II. Simulation and Expected Values
(a) Simulation
(b) Expected Values
Statistics Unit IV
I. Introduction to Inference
(a) What Is a Confidence Interval?
(b) What is a Test of Significance
(c) Use and Abuse of Statistical Inference
II. Inference for Tables and Means
(a) Two-Way Tables and the Chi-Square Test
(b) Inference about a Population Mean